1. Field of the Invention
The present invention relates to balanced modulators, and, more particularly, to a carrier rejection circuit for reducing
2. Description of the Related Art
A modulator circuit modulates a high-frequency carrier waveforth according to a modulating waveform to produce a modulated output signal. As shown in FIG. 1, such a modulator circuit includes a carrier signal port 10 to which a carrier signal LO(t) is applied, a modulating signal port 12 for receiving a modulating signal IF(t), and a modulated signal port 14 at which the modulated signal RF(t) is produced.
An ideal balanced modulator is one in which the modulated signal RF(t) is identically=0 when the voltage of the modulating signal IF(t)=0, regardless of the voltage of the carrier signal LO(t). Thus, in the ideal balanced modulator, a modulating signal IF(t)=0 will produce a modulated signal RF(t)=0, even if the carrier signal LO(t) is, for example, a normal sine wave.
Like the ideal balanced modulator, an ideal double-balanced modulator will produce a modulated signal RF(t)=0 when a modulating signal IF(t)=0 is applied. In addition, the ideal double-balanced modulator produces a modulated signal RF(t)=0 when the carrier signal LO(t)=0, independent of the modulating signal IF(t).
In practice, however, a balanced modulator circuit will produce an undesired modulated signal RF(t) even though the modulating signal IF(t)=0. As an example, an analog multiplier is one type of modulator that can be easily analyzed. The modulated signal RF(t) of the ideal analog multiplier modulator can be represented by the following equation: EQU RF(t)=k.times.LO(t).times.IF(t) (1)
where k is the gain constant of the multiplier. According to the above equation, it is apparent that the ideal multiplier is a double-balanced modulator, since RF(t)=0 when either LO(t) or IF(t)=0. However, if the practical multiplier circuit is subjected to a DC offset voltage VD at the modulating signal port 12, the above equation becomes: EQU RF(t)=k.times.LO(t).times.[IF(t)+VD] (2)
As a result, even if the modulating signal IF(t)=0, carrier leakage will occur due to the offset voltage VD, producing an undesirable modulated signal represented by: EQU RF(t)=k.times.LO(t).times.VD (3)
Another source of carrier leakage is parasitic coupling from the carrier signal port 10 to the modulated signal port 14 that is not coupled via the modulating circuit. For example, such parasitic coupling may be caused by stray capacitance, mutual inductance, or conductance effectively connected between the carrier signal port 10 and the modulated signal port 14.
In the case of carrier leakage caused by DC offset, if the carrier signal LO(t)=A.times.sin(wt), for example, the carrier leakage will be proportional to sin(wt), as evident from equation (3) above. This type of carrier leakage can be referred to as "in-phase" leakage. For parasitic coupling caused by stray capacitance, however, the carrier leakage will include a component proportional to cos(wt) resulting in "quadrature-phase" leakage. Parasitic in-phase leakage caused by conductance, for example, may be canceled by adjusting the offset voltage VD away from zero. However, because sine and cosine waves at the same frequency are linearly independent, it is not possible to cancel both the in-phase and quadrature-phase leakage terms by merely adjusting the offset voltage VD.